In Vigo's Case, the United States Supreme Court was asked to decide whether the United States had the right to seize a vessel owned by a Spanish citizen, Vigo, for alleged violations of the Neutrality Act of 1794. The Neutrality Act prohibited citizens of the United States from engaging in any hostile acts against a foreign nation with whom the United States was at peace. The Supreme Court held that the United States had the right to seize the vessel, as the Neutrality Act was a valid exercise of Congress' power to regulate foreign commerce. The Court also held that the seizure was not a violation of the Fifth Amendment, as the vessel was not taken for public use, but rather for the purpose of enforcing the law. The Court further held that the seizure was not a violation of the Fourth Amendment, as the seizure was not unreasonable or arbitrary. The Court noted that the seizure was necessary to prevent the vessel from being used to commit hostile acts against a foreign nation, and that the seizure was not done in an arbitrary or oppressive manner. Finally, the Court held that the seizure was not a violation of the Treaty of 1795 between the United States and Spain, as the treaty did not provide for the protection of Spanish vessels from seizure by the United States. The Court noted that the treaty only provided for the protection of Spanish vessels from seizure by other nations.

In Vigo's Case, the Supreme Court was asked to decide whether a federal court had jurisdiction over a case involving an alleged violation of the Neutrality Act. The majority opinion held that it did not have such jurisdiction because the act only applied to citizens and aliens who were present in or near U.S. territory at the time of their offense, and Vigo was neither a citizen nor an alien at that time. However, Justice Field dissented from this decision on two grounds: firstly, he argued that Congress intended for all persons within its territorial limits to be subject to its laws; secondly, he contended that since Vigo had been arrested within U.S. territory by officers acting under color of law then his arrest should be considered valid even if it violated international law or treaties with foreign nations as long as those violations occurred while enforcing domestic statutes enacted by Congress itself rather than through executive action alone without congressional authority behind them. In conclusion, Justice Field believed there was sufficient evidence for federal courts to exercise jurisdiction over cases like these where individuals are accused of violating acts passed by Congress regardless of their citizenship status or location when they committed their offenses